Illumination compensator for curved surface lithography

ABSTRACT

A zero power identical pair of oppositely-oriented meniscus lens elements mounted in the projection light path, serves as curved mask support while compensating for optical anomalies such as beam shift and beam deviations produced by other transparent supports for the curved mask. The zero-power meniscus lens pair, without affecting the transmission beam characteristics, lets the beam diffract as efficiently as does a regular planar mask, thus preserving the partial coherence effects and resolution concepts of projection lithography. This simple but novel optics device is not only expected to clear several barriers for curved mask projection lithography but also find place in other applications where collimated or converging light beams have to travel extra paths without significant aberration.

(B) CROSS-REFERENCE TO RELATED APPLICATIONS

This is a divisional application of U.S. patent application Ser. No.10/731,187, filed Dec. 09, 2003, now U.S. Pat. No. 7,106,415, issue dateNov. 12, 2006, Kuchibhotla et al., ILLUMINATION 10 COMPENSATOR FORCURVED SURFACE UTHOGRAPHY.

(C) STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

(Not Applicable)

(D) REFERENCE TO A MICROFICHE APPENDIX

(Not Applicable)

E) BACKGROUND OF THE INVENTION

(1) Field of the Invention

This invention relates to projection lithography systems for imagingonto curved substrates, and more particularly relates to a large-arealithography system featuring a curved mask that is identical in size andshape to the curved substrate. An axially moving 1:1 projection lensachieves a constant optical path length for conjugate image points inorder to maintain the substrate surface within the depth-of-focus,thereby providing an effective depth-of-focus much larger than thedepth-of-focus of the projection optics itself. This invention iscentered around a novel illumination compensator, a zero-power meniscuslens pair. Such a pair is part of an illumination system and protectsthe converging illumination beam from various image anomalies when ittransmits through a curved mask. This unique optical system withcurvatures on its elements has zero power and works like an non-tiltedplane glass blank in the path of a given collimated or convergent beam.A detailed paraxial ray theory was developed to demonstrate thefunctionality of such a device. Two possible configurations for Zerogona zero-power meniscus lens pair have been described in the invention.The unique device facilitates patterning on curved surfaces by means ofsmall-field seamless scanning techniques to achieve high resolution overan entire large-area curved substrate. The concept of compensationdescribed here is applicable in any generic optical system involved withillumination or imaging beams.

(2) Description of Related Art

Introduction to Optical Projection Lithography

In the recent past, electronics industry has witnessed dramatic increasein performance, throughput, yield and cost reduction with the advancesin optical projection lithography. On the other hand, detectortechnology promises tremendous future for curved focal plane arrays(FPAs) in strategic and astronomical applications. Contact andnon-contact projection lithography faces several challenges inpatterning intricate details on curved surfaces. Anvik's systems aredesigned based on a novel, hexagonal seamless scanning concept andsingle-planar stage system configuration that provide both high opticaland scanning efficiencies, and combine high-resolution imaging with verylarge exposure area capability. The prior art of Anvik's techniques forimaging on curved substrates has a curved mask that is identical in sizeand shape to the curved substrate for 1:1 patterning. There is a gooddescription of curved-mask lithography in U.S. Pat. No. 6,416,908,PROJECTION LITHOGRAPHY ON CURVED SUBSTRATES, Klosner, Zemel, Jain &Farmiga, Jul. 9, 2002. However, a curved mask, because of its finitethickness, can cause several image anomalies due to its interaction withthe illumination beam. In this invention, we propose and use a noveloptical device, which we call a zero-power meniscus lens pair. Such apair compensates for the image degradation associated with the use ofcurved masks.

Importance of the Illumination System

It has been a well-known fact from the times of invention of themicroscope that the resolution and contrast of the microscope aresignificantly influenced by the technique of illumination of the sample.Similarly, the illumination technique can make a significant impact onthe resolution and contrast of a lithographic projection system too.Though the illumination system is probably the most neglected or ignoredpart in such systems, some recent advances in illumination systems playgreat role in controlling the performance such as resolution, depth offocus and image contrast of a lithographic projection system. A few ofthese techniques are popularly known as off-axis illumination, annularsource illumination, slit source illumination, 2-point sourceillumination, SHRINC illumination and use of phase shift masks.

Brief Review of Existing Illumination Techniques for Planar Masks

It has been an established fact that the use of curved Focal PlaneArrays (FPAs) can significantly influence the space and militaryapplications in achieving wide fields-of-view for their sensors. Some ofthe techniques used for manufacturing these curved FPAs use curved masksin their projection systems. The several illumination techniquesdescribed above assume the use of planar masks in the object plane ofthe projection system. Use of curved masks in the object plane can causesevere image degradation due to defocus and beam deviations at thecurved object plane. Problems associated with defocus of the condensedbeam at the curved mask surface can be addressed by using special imagemotion compensating techniques within the condenser and the projectionlens. On the other hand, beam deviations at the curved mask surface cansignificantly impact the light coupling between condenser and theprojection lens affecting the partial coherence factor, which is theratio of numerical apertures of condenser and the projection lens. Apartial coherence factor value of 0.7 is normally chosen for incoherentillumination to achieve best resolution with projection lithography. Inthis paper, we describe a novel method to control the beam deviations atthe curved mask plane, thereby protecting the partial coherence factorand the resolution characteristics of the imaging system.

(F) BRIEF SUMMARY OF THE INVENTION

This invention provides to a large-area lithography system thecapability of patterning onto a curved substrate, using a curved mask inorder to achieve a fixed track length for conjugate object and imagepoints, by linearly moving a 1:1 projection lens for compensation on asmall-field seamless scanning platform, thereby maintaining the curvedsubstrate surface within its depth-of-focus, and by providing aneffective coupling of the illumination beam from the curved mask to theprojection lens, thereby preserving the partial coherence factor and therelated resolution characteristics 10 This invention provides thesecapabilities while retaining the option of small-field seamless scanningtechniques to achieve high resolution over the entire large-area curvedsubstrate.

The object of the invention is to make possible a high-resolutionprojection imaging operation on a curved substrate with topographicalvariations significantly greater than the depth-of-focus of the imagingoptics.

Another object of the invention is to permit scanning projectionimaging, by providing an effective solution for beam coupling mechanismusing an innovative optical system, a zero-power meniscus lens pair thatcarries the curved mask on one of its surfaces.

Another innovative feature of the invention is to provide a uniquedesign for zero-power meniscus lens pair, by means of a symmetricarrangement of two identical meniscus optical elements so that it worksas a null compensator for collimated or converging beams interactingwith a curved mask and thus causing negligible deviation or shift of thebeam passing through such a device.

An advantage of such unique configuration for a zero-power meniscus lenspair is that the design could be scaled up to conduct large-area curvedpatterning with relatively smaller cross-section of scanning convergentbeam imaging on one of its outer surfaces thus facilitating large-areaseamless scanning for curved-curved lithography.

Other objects, features and advantages of the invention will be apparentto those skilled in the art, in view of the drawings and writtendescription.

(G) BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 is a simplified semidiagrammatic elevation view of a preferredembodiment of the invention, showing a compensated curved mask with azero-power meniscus lens pair and curved substrate that lead to aneffective beam coupling,

FIG. 2 is a simplified semidiagrammatic elevation view of a PRIOR ARTimaging system similar to the preferred embodiment of the invention,showing uncompensated curved mask and curved substrate that lead to anineffective beam coupling in a folded mask-on-stage projectionembodiment of PRIOR ART.

FIG. 3 illustrates the basic illumination characteristics in projectionlithography, in which the mask, usually in the form of a grating,diffracts the incoming beam into zero-and-higher orders.

FIG. 4 is a PRIOR ART showing illumination characteristics in projectionlithography under coherent illumination.

FIG. 5 is a PRIOR ART showing illumination characteristics in projectionlithography under incoherent illumination.

FIG. 6 is a diagram showing how a meniscus lens shifts the light beamspassing through it, and if allowed to carry the mask on its outersurface, can cause an ineffective coupling of the illumination beam tothe projection lens.

FIG. 7 is a PRIOR ART diagram showing how the conventional lens paircalled the “Hypergon” acts as an imaging system and is significantlydifferent from a zero-power meniscus lens pair, in construction andperformance.

FIG. 8 is a diagram showing how a lens pair, such as the zero-powermeniscus lens pair, transmits the light beams without any deviations,and hence can provide an effective coupling of the illumination beam tothe projection lens.

FIG. 9 is an unfolded diagram showing how the zero-power meniscus lenspair, mask combination helps the projection lens collect the necessarydiffraction orders.

(H) DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 and FIG. 2 show the preferred embodiment for patterning ontocurved substrates by using a zero-power meniscus lens pair 1, mask 2having a curvature that is identical to that of the substrate 3 (i.e.,the size and shape of the mask 2 and substrate 3 are the same) byadditionally performing the imaging using a 1:1 projection imagingsystem featuring reverser 4, projection lens 5, and fold mirrors 6 asrequired in directing the patterning beam from illumination source 7 tosubstrate 3. Stage 8 provides scanning motion. All elements of FIG. 2(PRIOR ART) are also present in FIG. 1. The difference between thesystem of FIG. 1 and the PRIOR ART system of FIG. 2 is the presence ofthe zero-power meniscus lens pair 1, in FIG. 1 and the absence of thezero-power meniscus lens pair 1, in FIG. 2. The zero-power meniscus lenspair 1. in FIG. 1 provides an effective beam coupling between the curvedmask and the projection lens.

We hereby discuss the basis of our invention, initially dealing withplanar masks and then with the problems associated with thick curvedmasks. The discussions would finally evolve into the subject of thecurrent invention that significantly improves the performance of curvedmask lithography.

Patterning on Curved Surfaces Using an Anvik Seamless ScanningSystem—PRIOR ART—FIG. 2

FIG. 2 illustrates the configuration of a curved mask and curvedsubstrate when lithography is performed utilizing an Anvik large-areaseamless scanning microlithography system, as described in U.S. Pat. No.6,416,908, issued Jul. 9, 2002. The Anvik system uses a hexagonal imagefield to achieve seamless scanning, and a reverser unit, which maintainsthe required image orientation on the substrate. Elements of greatestsignificance in FIGS. 1 & 2 are: curved mask 2; curved substrate 3;reverser 4; projection lens 5, illumination source 7 and scanningplatform 8. The curved substrate 3 and curved mask 2 are situated on acommon scanning platform 8, simplifying the overall system design. Notethat since this is a seamless scanning system, the mask can besignificantly larger than the image field. When the Anvik system isconfigured using this invention for patterning a curved mask onto acurved substrate, the mask and substrate sit on the single scanningplatform, with the mask oriented in an inverted manner with respect tothe substrate. With this configuration, a constant track length ismaintained from any object point on the mask to its conjugate imagepoint on the substrate. Separate means of oppositely directed motionprovide motion to projection means 5 to correct defocus due to curvedobject surface and curved image surface. The illumination meanstypically includes condensing means having zoom capability to keep thesize and focus of the illumination beam constant on the mask.

Basic Illumination Characteristics

Illumination Systems with Planar Masks

All the lithographic tools based on optical projection lithographyemploy an illumination system that transmits uniform illuminationthrough a mask from a laser source to the projection lens. The mask,usually in the form of a grating, diffracts the incoming beam into zero-and higher orders depending on the period d of the mask, wavelength ofoperation λ and angle of incidence φ as given by the following relation,d(sin θ−sin φ)=nλ  (1)where θ is the angle of diffraction of order n. The spatial informationabout the mask is contained in the diffracted light. To achieve theperfect edge definition in the image plane all spatial frequencies ofthe mask must be captured by the projection lens and combined withzero-order beam at the image plane. Aerial image quality begins tosuffer when the projection lens can no longer transmit the higher-orderfrequencies. At the limit of resolution, only one or the both of thefirst-order beams are collected and combined with the zero-order beam.Beyond the resolution limit of the lens, the diffraction angle producedby the feature size is so large that the lens cannot transmit even thefirst-order beams and only the zero-order beam is transmitted producinga uniform irradiance in the image plane. The modulation or contrast andthus the resolution of the image is then totally lost beyond thetheoretical limit of resolution.

The resolution limit and contrast of the image are typically defined bythe degree of coherence of the illumination beam. In the coherent case,light is collimated perpendicular to the mask and the light diffractedthrough the mask with an angle θ is captured by the projection lensprovided θ≧NA of the projection lens. In the case of incoherentillumination, light can be diffracted at 2 NA and still be collected bythe projection lens so that the first-order beams can combine with thezero-order beam to provide the limited resolution. Thus, from equation(1) the highest spatial frequency ν_(max) that can be imaged by theprojection lens under coherent and incoherent illumination can bewritten as $\begin{matrix}{{v_{max\_ coherent} = {\frac{1}{d} = \frac{NA}{\lambda}}}{v_{max\_ incoherent} = {\frac{1}{d} = \frac{2{NA}}{\lambda}}}} & (2)\end{matrix}$

Though incoherent illumination provides twice the resolution as that ofcoherent illumination, higher spatial frequencies suffer from lowercontrast in the projected image under incoherent illumination. It hasbeen an established practice since the age of microscope to choose anoptimum partial degree of coherence σ between the two extremes tobalance the resolution and contrast. σ is often referred to as partialcoherence factor and is defined by the ratio of NA of illuminationsystem to that of projection system. $\begin{matrix}{\sigma = \frac{{NA}_{illumination}}{{NA}_{projection}}} & (3)\end{matrix}$

For cases of NA of illumination system tending to zero or a collimatedbeam, σ=0(coherent); and for cases where NA of illumination systemequals or becomes greater than that of projection system,σ≧1(incoherent). It is generally considered that the best illuminationfor optimum pattern transfer in conventional photoresists is by settinga σ value of ˜0.7 (partial coherence).

Problems Associated with Uncompensated Curved Masks

It is now easy to realize the importance of an effective couplingbetween illumination system and the projection lens by means of partialcoherence factor in the field of projection imaging. Use of planar masksat the intermediate focus obviously does not pose any challenge to anyprojection mechanism as they neither deviate nor distort the illuminatedbeam. On the other hand, a curved mask surface can significantly distortthe transmitting illuminating beam, depending on the structure of themask device, causing sever image anomalies and loss of resolution. Inthis invention, we enhance our prior art Anvik system for curved surfacelithography with a new illumination compensator that eliminatespractically all the problems associated with a curved mask.

Design of a Curved Mask Compensator

Design Principles of Such a Device

The basic goal of designing an illumination compensator for a curvedmask is to transmit the converging scanning beam undistorted in itsdirection and position of exit while it excurses over the curved maskduring scanning. The direction of the chief ray of the converging beamis preserved to maintain an effective coupling so that the lens collectsthe necessary diffracting orders. Angle of each ray with respect tochief ray within the converging beam is preserved to maintain thenumerical aperture of the illumination system, and thus the partialcoherence factor. This essentially calls for such an optical device,which holds the curved mask and acts like an optically powerlesscomponent as in the case of a planar mask. The basis of this inventionis centered on such an optical device that is transparent to theincoming radiation and holds the curved mask on one of its outer curvedsurfaces and transmits the radiation without any significant imageanomalies.

In this section we derive some basic relationships among theconstructional parameters of such a device. Let us think of a positivemeniscus element with its convex surface as the mask carrier for thepurpose. Initially, we derive some basic relations in the context ofusing such a single meniscus element. In the later part, we discuss somemajor advantages of using a symmetric meniscus doublet for holding acurved mask on one of its outer surfaces.

We derive here the basic paraxial relationships among the constructionalparameters to design and understand the behavior of meniscus elements inthe context of using them as illumination compensator. The equations arebased on the standard paraxial trace of a given ray within the opticalsystem. The symbols in these equations have the following meaning withsubscripts indicating the surface number under discussion.

u and u′ are the slopes of the ray before and after refraction at agiven surface;

y is the height of the ray on a surface;

t is the vertex spacing between two consecutive surfaces;

n and n′ are refractive indices of the medium before and afterrefraction

Meniscus Element:

Let the radii of curvature of the surfaces on a meniscus element be R₁and R₂. For a ray traveling at angle u₁ and striking the first surfaceat height y₁, the refraction is given by$u_{1}^{\prime} = {\frac{{nu}_{1}}{n^{\prime}} - \frac{y_{1}\left( {n^{\prime} - n} \right)}{R_{1}n^{\prime}}}$

For first element, n′=N and n=1, where N is the refractive index of theglass material of the element. Thus, $\begin{matrix}{u_{1}^{\prime} = {\frac{u_{1}}{N} - {\frac{\left( {N - 1} \right)}{N}\frac{y_{1}}{R_{1}}}}} & (4)\end{matrix}$The ray transfers and intersects the second surface at $\begin{matrix}{y_{2} = {{y_{1} + {t_{1}u_{1}^{\prime}}} = {\overset{\_}{1} - {\frac{\overset{\_}{N} - 1}{N}\left. \sqrt{}\frac{t_{1}}{\quad R_{1}} \right.\begin{matrix}\sqrt{} \\\sqrt{} \\

\end{matrix}y_{1}} + {\frac{t_{1}}{N}u_{1}}}}} & (5)\end{matrix}$Refraction at second surface may now similarly be derived as eqn.(4) andon simplification we get, $\begin{matrix}{u_{2}^{\prime} = {u_{1} - {\left( {N - 1} \right)\frac{y_{1}}{R_{1}}} - \frac{y_{2}}{R_{2}}}} & (6)\end{matrix}$

At this moment it is worth making a note on the performance of a singlemeniscus element with ray entering on concave surface and emitting fromthe convex surface as shown in FIG. 6. In order to perform likenon-deviating element for a given ray with slope u₁, we would like tohaveu₂′=u₁and, Eqn.(6) would then give $\begin{matrix}{\frac{y_{1}}{R_{1}} = \frac{y_{2}}{R_{2}}} & (7)\end{matrix}$On substitution of Eqn.(5) in Eqn.(7), we get $\begin{matrix}{{R_{1} - R_{2}} = {{\frac{\left( {N - 1} \right)}{N}t_{1}} - \frac{t_{1}u_{1}R_{1}}{{Ny}_{1}}}} & (8)\end{matrix}$

As explained earlier, the objective of designing this optical system isto transmit the collimated or converging beam undeviated without anylateral shift when the optical system moves perpendicular to its opticalaxis. In the case of a single meniscus Eqn. (8) is never satisfied, asthe constructional parameter ΔR (i.e., R₁—R₂) is a function of boththickness and u₁. The dependence of ΔR on u₁ can only be eliminated forcollimated beam for which u₁=0. However, for the ray in a convergentbeam with u₁≢0, Eqn. (7) is never satisfied and u₂′≢u₁, affectingpartial coherence factor when the convergent beam excurses over a curvedsurface. The dependence of ΔR on t₁ is possible for a meniscus withidentical radii of curvature with zero thickness. It is, however, hardto realize such a meniscus optical element with negligible thicknesscapable of transmitting UV radiation.

On the other hand, a meniscus element with finite thickness can be madeto have selected radii of curvature in compliance with Eqn. (8) so thatthe element would not deviate an axial or collimated ray (with u₁=0)after refraction through the element. That is, $\begin{matrix}{{\Delta\quad R} = {{R_{1} - R_{2}} = {\frac{\left( {N - 1} \right)}{N}t_{1}}}} & (9)\end{matrix}$However, for a beam with ΔR given by Eqn. (9), Eqn. (5) gives us,$\begin{matrix}{{\Delta\quad y} = {{y_{1} - y_{2}} = {{\frac{\left( {N - 1} \right)}{N}\frac{t_{1}y_{1}}{R_{1}}} = \frac{\Delta\quad{Ry}_{1}}{R_{1}}}}} & {(10)F}\end{matrix}$

Even for collimated beams with u₁=0, Eqn. (10) still predicts theunwanted lateral shift Δy. In summary, Equs.(6)-(10) describe that asingle meniscus element with finite thickness needs to have differentradius of curvature on each of its surfaces as given by Eqn.(9) to makethe ray of a collimated beam undeviated after passing through theelement. However, for the ray in a convergent beam with u₁≢0, Eqn. (7)is never satisfied and affects the numerical aperture and also thepartial coherence factor especially when the convergent beam excursesover a curved surface. Also, the ray undergoes a lateral shift Δy asgiven by Eqn. (10) that is a function of ray height y₁ on front surface.Thus a single meniscus element suffers from both drawbacks of deviatingand shifting the ray laterally on second surface depending on the rayangle and its height on first surface. This is very undesirable forscanning systems such as seamless scanning technique because the beam orthe ray excurses nonuniformly over the second surface. This would callfor a complicated scanning mechanism to make the beam travel uniformlyon the curved surface. Hence, a single meniscus element would not servethe required purpose of an illumination compensator for curved masks inmaking the beam transmit without deviation or shift.

The Goerz Hypergon lens (U.S. Pat. No. 706,650), a traditionalphotographic objective, consists of two symmetrical menisci equidistanton either side of the aperture stop. The inner and outer radii ofcurvature of the Goerz Hypergon differ by only one-half percent,producing a very flat Petzval curvature even at very large field ofview. The aperture stop between the menisci is important in the GoerzHypergon lens; this arrangement generates lens power as shown in FIG. 7.However, in the current application we need to project the condensedbeam onto a curved surface of an optical system, which on refractionwould not deviate the beam. This calls for a zero-power optical system,the outer surface on which the converging illumination beam is in focus,scans the curved surface with the help of unitary stage. In other words,we need to consider an optical system with diameter larger than thescanning beam. The purpose of such an optical device is not to deviatethe transmitted beam on exit. This can only be achieved by transmittingthe beam through a zero-power optical device as that of a plane parallelplate. In this section, we discuss the design and function of such adevice that we will call zero-power meniscus lens pair 1. The zero-powermeniscus lens pair 1 has an outer curved surface and would not deviatenor shift the beam laterally on transition. In the current application,the outer curved surface of the zero-power meniscus lens pair 1 carriesthe curved mask 2.

The zero-power meniscus lens pair 1 has two identical menisci with theirradii of curvature set by Eqn. (9) and the elements grouped in closeproximity, with their concave surfaces facing each other as shown inFIG. 8. The outer surface holds the flexible mask 2 close enough using alocking band 9. The goal of designing such an optics device is to makethe small-sized illuminating beam transmit through the optic at anyheight from the optical axis of the zero-power meniscus lens pair 1,without any deviation or shift to preserve the concept of providingconstant partial coherence factor for the sake of obtaining betterresolution and contrast in curved mask lithography. As proved in thissection, the symmetry of the configuration cancels out the lateralshifts introduced by each meniscus without deviating the ray through thesystem and thus preserving the numerical aperture of the condenser andresolution characteristics of the projection system. Notice that thelookalike Hypergon on the other hand, is an imaging system as shown inFIG. 7, with construction and performance significantly different fromthat of the zero-power meniscus lens pair 1. FIG. 7 shows how theHypergon of PRIOR ART has lens power. FIG. 9 shows how the placement ofthe mask 2 on the convex exit surface of the zero-power meniscus lenspair 1, with the focus on the curved mask 2, allows for proper focus ofthe projected beam onto the curved substrate 3.

We may now extend the above raytracing equations to zero-power meniscuslens pair 1. In order to work out a zero-power meniscus lens pair 1, letus consider a lens doublet of two identical menisci with concavesurfaces facing each other. Let us assume that the second meniscuselement, separated from the first meniscus by a distance t₂, has radiiof curvature R₃ and R₄ and thickness t₃. The transfer equation to thirdsurface may now be written asy ₃ =y ₂ +t ₂ u ₂ ′  (11)and refraction at third surface yields $\begin{matrix}{u_{3}^{\prime} = {\frac{{nu}_{3}}{n^{\prime}} - \frac{y_{3}\left( {n^{\prime} - n} \right)}{R_{3}n^{\prime}}}} & (12)\end{matrix}$In view of identical menisci for zero-power meniscus lens pair, we canwrite

-   -   n=1,n′=N and u₃=u₂′ for third surface;    -   n=N, n′=1 and u₄=u₃′ for fourth surface;    -   R₃=—R₂ and R₄=—R₁ and t₃=t₁.        Substitution of Eqn.(11) in the above equation gives us u 3 ′ =        1 N + - 1 N ⁢ √ t 2 ⁢ u 2 ′ + - 1 N ⁢ √ y 2 ( 13 )        Transfer to fourth surface may now be written as        y ₄ =y ₃ +t ₃ u ₃′        Substitution of Equs.(11)-(13) and further simplification leads        to $\begin{matrix}        {y_{4} = {1 + {\begin{matrix}        {- 1} \\

        \end{matrix}\begin{matrix}        {{}_{}^{}{}_{}^{}} \\

        \end{matrix}y_{2}} + t_{2} + {t_{1}\begin{matrix}         \\

        \end{matrix}} + {\begin{matrix}        {- 1} \\

        \end{matrix}\begin{matrix}        {{}_{}^{}{}_{}^{}} \\

        \end{matrix}\begin{matrix}        \overset{\sqrt{}}{\sqrt{}} \\

        \end{matrix}u_{2}^{\prime}}}} & (14)        \end{matrix}$        For an axial ray or ray incident at a height y, from optical        axis with u₁=0 and thus u₂′=0, Equs. (6), (7) and (9) yield        $y_{4} = {{1 + {\frac{\Delta\quad R}{R_{2}}y_{2}}} = y_{1}}$        Thus a zero-power meniscus lens pair would not cause any shift        in the height of the axial ray unlike a single meniscus lens.        Now, let us see the deviation of a ray produced by the device.

The equation for refraction at fourth surface may now be written as$\begin{matrix}{u_{4}^{\prime} = {\frac{{nu}_{4}}{n^{\prime}} - \frac{y_{4}\left( {n^{\prime} - n} \right)}{R_{4}n^{\prime}}}} \\{= {{Nu}_{3}^{\prime} - {\frac{\left( {N - 1} \right)}{R_{1}}y_{4}}}}\end{matrix}$Use of Eqns. (13) and (14) in the above equation and furthersimplification yields $\begin{matrix}{u_{4}^{\prime} = {1 + {\frac{\left( {N - 1} \right)t_{2}}{R_{1}R_{2}}\Delta\quad R} - {\frac{\left( {N - 1} \right)}{N}t_{1}} - {\frac{\left( {N - 1} \right)}{N}\frac{t_{1}}{R_{1}}u_{2}^{\prime}} +}} \\{{\frac{\left( {N - 1} \right)}{R_{1}R_{2}}\Delta\quad R} - {\frac{\left( {N - 1} \right)}{N}t_{1}y_{2}}}\end{matrix}$Using Eqn.(6) for u₂′ and Eqn.(5) for y₂ there in, we get$\begin{matrix}\begin{matrix}{u_{4}^{\prime} = {\left\lbrack {1 + {\frac{\left( {N - 1} \right)t_{2}}{R_{1}R_{2}}\left( {{\Delta\quad R} - {\frac{\left( {N - 1} \right)}{N}t_{1}}} \right)} - {\frac{\left( {N - 1} \right)}{N}\frac{t_{1}}{R_{1}}}} \right\rbrack \times}} \\{\left\lbrack {{\left( {1 + {\frac{\left( {N - 1} \right)}{N}\frac{t_{1}}{R_{2}}}} \right)u_{1}} - {\left( {N - 1} \right)\left( {{\Delta\quad R} - {\frac{\left( {N - 1} \right)}{N}t_{1}}} \right)\frac{y_{1}}{R_{1}R_{2}}}} \right\rbrack +} \\{\frac{\left( {N - 1} \right)}{R_{1}R_{2}}\left( {{\Delta\quad R} - {\frac{\left( {N - 1} \right)}{N}t_{1}}} \right)y_{2}}\end{matrix} & (15)\end{matrix}$It is now easy to explain how Eqn.(9) could help a zero-power meniscuslens pair 1 achieve the function of the required illuminationcompensator without deviation and shift of a ray. When Eqn.(9) issatisfied, Eqn.(15) can be simplified to $\begin{matrix}\begin{matrix}{u_{4}^{\prime} = {\left( {1 - {\frac{\left( {N - 1} \right)}{N}\frac{t_{1}}{R_{1}}}} \right)\left( {1 + {\frac{\left( {N - 1} \right)}{N}\frac{t_{1}}{R_{2}}}} \right)u_{1}}} \\{= {\left( {1 - \frac{\Delta\quad R}{R_{1}}} \right)\left( {1 + \frac{\Delta\quad R}{R_{2}}} \right)u_{1}}} \\{= u_{1}}\end{matrix} & (16)\end{matrix}$A Numerical Example

The zero-power meniscus lens pair worksheet below illustrates thecalculations for a sample zero-power meniscus lens pair 1, worked outfor an outer radius of curvature of R=50 mm and thickness of 10 mm. Thecalculations were done for a displaced axial ray and an off-axial rayentering the lens with an angle. Initially it is required to compute theinner radius of curvature of the meniscus elements for a given value ofradius on the outer surface using Eqn. (9) and then the above set ofequations or any standard optical design software can be used toevaluate the design. The paraxial raytrace values of a given ray asgiven in the table may be compared with the real raytrace values thatfall in close agreement with each other. Parameter/i 0 1 2 3 4 t_(i)10.000 12.000 10.000 n_(i)′ 1.509 1.000 1.509 1.000 R_(i) −50.000−46.627 46.627 50.000 y_(i) 12.500 11.657 11.657 12.500 u_(i) 0.0000.000 −0.084 −0.084 0.000 y_(pi) 10.632 8.011 1.848 −0.061 u′_(pi)−0.276 −0.254 −0.294 −0.187 −0.276

It may be seen that the zero-power meniscus lens pair 1 preserves y_(i),u_(i), and u′_(pi) of any given ray on first and fourth surfaces, havingthe same functional properties as that of a plane parallel plate. Infact, it is easier to prove and visualize the zero-power meniscus lenspair 1 as equivalent to a pair of plane parallel plates separated by thesame distance as that of menisci in zero-power meniscus lens pair 1. Theoptical path length variation for any arbitrary ray in meniscus elementsis compensated by the altered air path between the menisci.

An application of the zero-power meniscus lens pair 1 is its use atintermediate curved image surfaces with the image surface falling onzero-power meniscus lens pair 1's outer surface whose radius ofcurvature could be designed to the field curvature of the optics infront of the zero-power meniscus lens pair 1. The description andexample above emphasize its behavior equivalent to that of a planeparallel plate with curved surfaces. Hence, wherever a plane parallelplate has to be replaced by an optic with curved surfaces, thezero-power meniscus lens pair 1 could be used without affecting theperformance of whole system.

Use of Zero-Power Meniscus Lens Pair 1 for Curved Lithography.

As described earlier, the illuminated beam from the condenser could beeffectively coupled to the projection lens by resting the curved mask onan optical device that transmits the beam undistorted. A zero-powermeniscus lens pair 1, with its outer radius of curvature to match withthat of the substrate and a membrane mask, that is proprietary to Anviktechnology, will be precisely stretched and secured over the outersurface by a frame to fix its position. The zero-power meniscus lenspair 1-curved mask combination works just like that of a planar maskproviding an efficient coupling between illumination system and theimaging system for curved lithography. FIG. 9 is a schematic of thefunctionality of the zero-power meniscus lens pair 1/_mask combinationand how the necessary diffraction orders are collected by the projectionlens.

Conclusion

Special Merits of the Curved Mask Compensator

The illumination system is a very important part of the lithographictool. It plays an important role in controlling the performance of thelithographic system. The field of projection lithography using planarmasks and substrates has witnessed several important innovations in thefield of illumination engineering that significantly improved theresolution and contrast of projection patterning. Projection lithographyon curved substrates needs efficient illumination techniques toilluminate curved masks. The illuminating beam displaced and deviated bythe bulk of a thick curved mask when used alone, needs to have acompensator in front of the mask for best results.

We discussed a novel optics device, called zero-power meniscus lens pair1, that has curved optical elements exhibiting zero total power andperforms as good as a plane parallel plate causing no deviations to theincoming radiation. Having this unique null property zero-power meniscuslens pair 1 is expected to serve various applications as an alternativeto plane parallel plate. We also use the zero-power meniscus lens pair 1with curved mask on one of its outer surfaces, making the whole devicevery efficient in coupling the illumination beam to the imaging system.

Another important merit of this invention is that the two meniscuselements can also be arranged back-to-back on convex surfaces withconcave outer surfaces and make the device still carry the sameproperties described above for zero-power meniscus lens pair 1. Henceeither configuration could be referred to as part of the presentinvention.

1. A projection lithography system having a zero-power meniscus lenspair (1) as mask support for a flexible film curved mask.
 2. Aprojection lithography system according to claim 1, in which saidzero-power meniscus lens pair (1) has an exit face, and said exit faceserves as mask support for a flexible film curved mask.
 3. A curved mask(2) for a projection lithography system, for use in imaging a patternfrom its surface to the surface of a curved substrate of known curvaturecharacterized by: a) an optically transparent mask body having surfacecurvature identical to said known curvature of the substrate, having aphoto-opaque pattern layer at said surface; and b) means forming azero-power meniscus lens pair (1) with said mask body by mounting anoppositely oriented optically transparent compensating body in closeproximity in the light path.
 4. A curved mask (2) according to claim 3,wherein said optically transparent mask body and said opticallytransparent compensating body are of fused silica.
 5. A projectionlithography mask according to claim 4 having a photo-opaque patternlayer selected from aluminum and chrome on said curved mask (12).
 6. Aprojection lithography mask made by the following contactlithography/non-contact lithography process, starting with a planar maskof metal-on-quartz; 1) Place a layer of photo-active material onaluminized polypropylene in contact with said planar mask; 2) Expose toimaging radiation; 3) Process to provide a pattern of aluminum on aflexible film of polypropylene; 4) Place the patternedaluminum-on-polypropylene in contact with a hard, curved opticallytransparent blank projection mask resting on a zero-power meniscus lenspair.
 7. A projection lithography mask made by the process of claim 6,wherein the hard, curved optically transparent blank of step 4 isprecooked with a metallized layer and a photoactive resist layer, toserve as an intermediate, and steps are added as follows: 5) Expose forimaging defined by the pattern; 6) Process to develop the pattern as ametal-on-optic curved mask; and 7) Replicate by projection printingusing said metal-on-optic curved projection mask to fabricate ametal-on-optic curved projection mask.
 8. A zero power lens groupcomprising paired identical meniscus lenses arranged to carry apatterned mask for input to a projection lens so as to transmit theillumination beam without deviation and displacement to ensure highresolution pattern transfer in curved mask lithography.
 9. A zero powerlens group according to claim 8, arranged to serve as a curved mask/masksupport subassembly for use in projection lithography, having twomeniscus elements, one of which meniscus elements having a curved outerface equipped with a similarly-curved photo-opaque pattern means.
 10. Azero power lens group according to claim 9, having a concave outersurface carrying a photo-opaque pattern.
 11. A zero power lens groupaccording to claim 9 having a convex outer surface carrying aphoto-opaque pattern.
 12. A zero power lens group having back-to-backcomplementary lens elements serving as a zero-power optical device, at aposition with respect to the optical axis in the optical system totransmit collimated and uncollimated beams without deviation and withoutshift from the line of propagation.